If you have a no start situation, check for ignition, injection and fuel pump operation. If none of the above operate then the supplies and earth's as well as the crankshaft trigger inputs need to be tested. Because the E36 has the DME mounted inside the plenum chamber behind the firewall, it is common for it to become water damaged when the plenum chamber drain pipes get blocked and water enters the DME. It is recommended to check these drain pipes when replacing a DME.
The DME in an E36 can be accessed by removing the plate on the firewall behind the left hand shock tower.

Power feed circuit
pin 26 - constant 12v feed from the battery
pin 54 - power in from DME main relay
pin 56 - ignition key power, only has power when key on

When the ignition key is turned on, power is supplied to pin 56. The DME will then supply an earth at pin 27 for the DME main relay to pull in. When this relay pulls in, power is then supplied to pin 54 via the contacts of the relay.
When the engine is running and the key is turned off, injection and fuel pump stop immediately. After the engine has finally stopped rotating the DME will then stop supplying an earth for the main relay on pin 27. Therefore the relay will open and stop supplying power to pin 54.